Optimal approximation of stochastic differential equations with additive fractional noise:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Aachen
Shaker
2006
|
| Schriftenreihe: | Mathematik
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 111 S. |
| ISBN: | 3832250832 9783832250836 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV021792764 | ||
| 003 | DE-604 | ||
| 005 | 20070116 | ||
| 007 | t | ||
| 008 | 061102s2006 m||| 00||| eng d | ||
| 020 | |a 3832250832 |9 3-8322-5083-2 | ||
| 020 | |a 9783832250836 |9 978-3-8322-5083-6 | ||
| 035 | |a (OCoLC)179938471 | ||
| 035 | |a (DE-599)BVBBV021792764 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-824 |a DE-634 | ||
| 084 | |a SK 470 |0 (DE-625)143241: |2 rvk | ||
| 100 | 1 | |a Neuenkirch, Andreas |d 1976- |e Verfasser |0 (DE-588)13170141X |4 aut | |
| 245 | 1 | 0 | |a Optimal approximation of stochastic differential equations with additive fractional noise |c Andreas Neuenkirch |
| 264 | 1 | |a Aachen |b Shaker |c 2006 | |
| 300 | |a 111 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Mathematik | |
| 502 | |a Zugl.: Darmstadt, Techn. Univ., Diss., 2006 | ||
| 650 | 7 | |a Équations différentielles - Congrès |2 ram | |
| 650 | 0 | 7 | |a Gebrochene Brownsche Bewegung |0 (DE-588)4780019-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Rauschen |0 (DE-588)4048606-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Approximation |0 (DE-588)4002498-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |D s |
| 689 | 0 | 1 | |a Rauschen |0 (DE-588)4048606-0 |D s |
| 689 | 0 | 2 | |a Gebrochene Brownsche Bewegung |0 (DE-588)4780019-7 |D s |
| 689 | 0 | 3 | |a Approximation |0 (DE-588)4002498-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch Darmstadt |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015005376&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-015005376 | ||
Datensatz im Suchindex
| _version_ | 1804135704441126912 |
|---|---|
| adam_text | OPTIMAL APPROXIMATION OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH ADDITIVE
FRACTIONAL NOISE VOM FACHBEREICH MATHEMATIK DER TECHNISCHEN UNIVERSITAT
DARMSTADT ZUR ERLANGUNG DES GRADES EINES DOKTORS DER NATURWISSENSCHAFTEN
(DR. RER. NAT.) GENEHMIGTE DISSERTATION VON DIPL.-MATH. ANDREAS
NEUENKIRCH AUS OFFENBACH AM MAIN REFERENT: KORREFERENT: TAG DER
EINREICHUNG: TAG DER MIINDLICHEN PRIIFUNG: DARMSTADT D17 PROF. DR. K.
RITTER PROF. DR. P.E. KLOEDEN 6. DEZEMBER 2005 16. FEBRUAR 2006 2006
CONTENTS 1 INTRODUCTION 7 1.1 MAIN RESULTS 8 1.1.1 ONE-POINT
APPROXIMATION 8 1.1.2 GLOBAL APPROXIMATION 9 1.2 NOTATION 12 2
PRELIMINARIES 13 2.1 SDES WITH ADDITIVE FRACTIONAL NOISE 13 2.2 REMARKS
16 2.3 PROOFS 17 2.3.1 PROOF OF PROPOSITION 1 17 2.3.2 PROOF OF
PROPOSITION 2 20 3 ONE-POINT APPROXIMATION 21 3.1 NON-EQUIDISTANT
WAGNER-PLATEN-TYPE SCHEME 21 3.2 LOWER BOUNDS 24 3.3 EXAMPLE 26 3.4
REMARKS 27 3.5 PROOFS 29 3 4 CONTENTS 3.5.1 WAGNER-PLATEN SCHEME 30
3.5.2 PRELIMINARIES FOR THE WAGNER-PLATEN-TYPE SCHEME 40 3.5.3 THE
INTEGRATION PROBLEM AND PROOF OF THEOREM 1 48 3.5.4 PROOF OF COROLLARY 1
66 3.5.5 PROOF OF THEOREM 2 69 4 GLOBAL APPROXIMATION 73 4.1
NON-EQUIDISTANT EULER SCHEME 73 4.2 LOWER BOUNDS 75 4.3 EXAMPLE 77 4.4
REMARKS 77 4.5 PROOFS 79 4.5.1 PRELIMINARIES FOR THE PROOF OF THEOREM 3
79 4.5.2 PROOF OF THEOREM 3 84 4.5.3 PRELIMINARIES FOR THE PROOF OF
THEOREM 4 85 4.5.4 PROOF OF THEOREM 4 86 4.5.5 DISCUSSION OF THE PROOF
OF THEOREM 4 87 4.5.6 THE EULER SCHEME FOR THE LANGEVIN EQUATION:
ONE-POINT ERROR 89 5 OUTLOOK: NON-ADDITIVE NOISE 91 A FRACTIONAL
STOCHASTIC CALCULUS 95 A.I GENERALIZED STIELTJES INTEGRATION 95 A.2
MALLIAVIN CALCULUS FOR FRACTIONAL BROWNIAN MOTION 97 A.2.1 FRACTIONAL
BROWNIAN MOTION 97 CONTENTS 5 A.2.2 MALLIAVIN DERIVATIVE 98 A.2.3
SKOROHOD INTEGRATION 99 A.2.4 TRANSFER PRINCIPLE 100 A.2.5 WIENER CHAOS
DECOMPOSITION 102 B EXACT ERROR FORMULAS 103 B.I ONE-POINT APPROXIMATION
103 B.2 GLOBAL APPROXIMATION 104 BIBLIOGRAPHY 107
|
| adam_txt |
OPTIMAL APPROXIMATION OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH ADDITIVE
FRACTIONAL NOISE VOM FACHBEREICH MATHEMATIK DER TECHNISCHEN UNIVERSITAT
DARMSTADT ZUR ERLANGUNG DES GRADES EINES DOKTORS DER NATURWISSENSCHAFTEN
(DR. RER. NAT.) GENEHMIGTE DISSERTATION VON DIPL.-MATH. ANDREAS
NEUENKIRCH AUS OFFENBACH AM MAIN REFERENT: KORREFERENT: TAG DER
EINREICHUNG: TAG DER MIINDLICHEN PRIIFUNG: DARMSTADT D17 PROF. DR. K.
RITTER PROF. DR. P.E. KLOEDEN 6. DEZEMBER 2005 16. FEBRUAR 2006 2006
CONTENTS 1 INTRODUCTION 7 1.1 MAIN RESULTS 8 1.1.1 ONE-POINT
APPROXIMATION 8 1.1.2 GLOBAL APPROXIMATION 9 1.2 NOTATION 12 2
PRELIMINARIES 13 2.1 SDES WITH ADDITIVE FRACTIONAL NOISE 13 2.2 REMARKS
16 2.3 PROOFS 17 2.3.1 PROOF OF PROPOSITION 1 17 2.3.2 PROOF OF
PROPOSITION 2 20 3 ONE-POINT APPROXIMATION 21 3.1 NON-EQUIDISTANT
WAGNER-PLATEN-TYPE SCHEME 21 3.2 LOWER BOUNDS 24 3.3 EXAMPLE 26 3.4
REMARKS 27 3.5 PROOFS 29 3 4 CONTENTS 3.5.1 WAGNER-PLATEN SCHEME 30
3.5.2 PRELIMINARIES FOR THE WAGNER-PLATEN-TYPE SCHEME 40 3.5.3 THE
INTEGRATION PROBLEM AND PROOF OF THEOREM 1 48 3.5.4 PROOF OF COROLLARY 1
66 3.5.5 PROOF OF THEOREM 2 69 4 GLOBAL APPROXIMATION 73 4.1
NON-EQUIDISTANT EULER SCHEME 73 4.2 LOWER BOUNDS 75 4.3 EXAMPLE 77 4.4
REMARKS 77 4.5 PROOFS 79 4.5.1 PRELIMINARIES FOR THE PROOF OF THEOREM 3
79 4.5.2 PROOF OF THEOREM 3 84 4.5.3 PRELIMINARIES FOR THE PROOF OF
THEOREM 4 85 4.5.4 PROOF OF THEOREM 4 86 4.5.5 DISCUSSION OF THE PROOF
OF THEOREM 4 87 4.5.6 THE EULER SCHEME FOR THE LANGEVIN EQUATION:
ONE-POINT ERROR 89 5 OUTLOOK: NON-ADDITIVE NOISE 91 A FRACTIONAL
STOCHASTIC CALCULUS 95 A.I GENERALIZED STIELTJES INTEGRATION 95 A.2
MALLIAVIN CALCULUS FOR FRACTIONAL BROWNIAN MOTION 97 A.2.1 FRACTIONAL
BROWNIAN MOTION 97 " CONTENTS 5 A.2.2 MALLIAVIN DERIVATIVE 98 A.2.3
SKOROHOD INTEGRATION 99 A.2.4 TRANSFER PRINCIPLE 100 A.2.5 WIENER CHAOS
DECOMPOSITION 102 B EXACT ERROR FORMULAS 103 B.I ONE-POINT APPROXIMATION
103 B.2 GLOBAL APPROXIMATION 104 BIBLIOGRAPHY 107 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Neuenkirch, Andreas 1976- |
| author_GND | (DE-588)13170141X |
| author_facet | Neuenkirch, Andreas 1976- |
| author_role | aut |
| author_sort | Neuenkirch, Andreas 1976- |
| author_variant | a n an |
| building | Verbundindex |
| bvnumber | BV021792764 |
| classification_rvk | SK 470 |
| ctrlnum | (OCoLC)179938471 (DE-599)BVBBV021792764 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Thesis Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01889nam a2200445 c 4500</leader><controlfield tag="001">BV021792764</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20070116 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">061102s2006 m||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3832250832</subfield><subfield code="9">3-8322-5083-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783832250836</subfield><subfield code="9">978-3-8322-5083-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)179938471</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV021792764</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-824</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 470</subfield><subfield code="0">(DE-625)143241:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Neuenkirch, Andreas</subfield><subfield code="d">1976-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)13170141X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Optimal approximation of stochastic differential equations with additive fractional noise</subfield><subfield code="c">Andreas Neuenkirch</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Aachen</subfield><subfield code="b">Shaker</subfield><subfield code="c">2006</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">111 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Mathematik</subfield></datafield><datafield tag="502" ind1=" " ind2=" "><subfield code="a">Zugl.: Darmstadt, Techn. Univ., Diss., 2006</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Équations différentielles - Congrès</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gebrochene Brownsche Bewegung</subfield><subfield code="0">(DE-588)4780019-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Rauschen</subfield><subfield code="0">(DE-588)4048606-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastische Differentialgleichung</subfield><subfield code="0">(DE-588)4057621-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Approximation</subfield><subfield code="0">(DE-588)4002498-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4113937-9</subfield><subfield code="a">Hochschulschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Stochastische Differentialgleichung</subfield><subfield code="0">(DE-588)4057621-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Rauschen</subfield><subfield code="0">(DE-588)4048606-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Gebrochene Brownsche Bewegung</subfield><subfield code="0">(DE-588)4780019-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Approximation</subfield><subfield code="0">(DE-588)4002498-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS Datenaustausch Darmstadt</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015005376&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-015005376</subfield></datafield></record></collection> |
| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV021792764 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T15:45:03Z |
| indexdate | 2024-07-09T20:44:44Z |
| institution | BVB |
| isbn | 3832250832 9783832250836 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015005376 |
| oclc_num | 179938471 |
| open_access_boolean | |
| owner | DE-824 DE-634 |
| owner_facet | DE-824 DE-634 |
| physical | 111 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Shaker |
| record_format | marc |
| series2 | Mathematik |
| spelling | Neuenkirch, Andreas 1976- Verfasser (DE-588)13170141X aut Optimal approximation of stochastic differential equations with additive fractional noise Andreas Neuenkirch Aachen Shaker 2006 111 S. txt rdacontent n rdamedia nc rdacarrier Mathematik Zugl.: Darmstadt, Techn. Univ., Diss., 2006 Équations différentielles - Congrès ram Gebrochene Brownsche Bewegung (DE-588)4780019-7 gnd rswk-swf Rauschen (DE-588)4048606-0 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Stochastische Differentialgleichung (DE-588)4057621-8 s Rauschen (DE-588)4048606-0 s Gebrochene Brownsche Bewegung (DE-588)4780019-7 s Approximation (DE-588)4002498-2 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015005376&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Neuenkirch, Andreas 1976- Optimal approximation of stochastic differential equations with additive fractional noise Équations différentielles - Congrès ram Gebrochene Brownsche Bewegung (DE-588)4780019-7 gnd Rauschen (DE-588)4048606-0 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4780019-7 (DE-588)4048606-0 (DE-588)4057621-8 (DE-588)4002498-2 (DE-588)4113937-9 |
| title | Optimal approximation of stochastic differential equations with additive fractional noise |
| title_auth | Optimal approximation of stochastic differential equations with additive fractional noise |
| title_exact_search | Optimal approximation of stochastic differential equations with additive fractional noise |
| title_exact_search_txtP | Optimal approximation of stochastic differential equations with additive fractional noise |
| title_full | Optimal approximation of stochastic differential equations with additive fractional noise Andreas Neuenkirch |
| title_fullStr | Optimal approximation of stochastic differential equations with additive fractional noise Andreas Neuenkirch |
| title_full_unstemmed | Optimal approximation of stochastic differential equations with additive fractional noise Andreas Neuenkirch |
| title_short | Optimal approximation of stochastic differential equations with additive fractional noise |
| title_sort | optimal approximation of stochastic differential equations with additive fractional noise |
| topic | Équations différentielles - Congrès ram Gebrochene Brownsche Bewegung (DE-588)4780019-7 gnd Rauschen (DE-588)4048606-0 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Équations différentielles - Congrès Gebrochene Brownsche Bewegung Rauschen Stochastische Differentialgleichung Approximation Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015005376&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT neuenkirchandreas optimalapproximationofstochasticdifferentialequationswithadditivefractionalnoise |